Submissions must be either Requests or Suggests. Anything else gets removed. Television suggestions go to r/televisionsuggestions.

Requests - If you wish to use an alternative to text; such as a picture, music or video, it must be in the body of your post.

Suggests - Be clearly labelled; a single Suggestion; with the title; indicate if still in theatres; use neutral sources only, this subreddit isn't your link farm; such as, Letterboxd, Rotten Tomatos or IMDB; pictures, music or video must be in the body of your post; and, wait six months prior to posting a previously suggested movie. Do not post any film that is Barred, which is listed in the Sticky.

It takes a fantastical, terrifying story…and grounds it in the real world.

This movie does that with a different kind of fantastical story involving omens and clairvoyance. It sets up a lot of clues leading to the ending and the conclusion of the mystery, but rather than M. Night scattering Easter eggs throughout The Sixth Sense that have no roots in the plot, Nicolas Roeg does just that and has everything that comes the story's way—even the film's poster!—point towards its great ending.

It's pretty long—110 minutes—and the plot will seem to move as slow as a wet sponge, but if you really stick with it and keep your eyes peeled on everything in every shot at every second; Be warned, this is not a light watch and you must be paying attention at all times to enjoy it.

A lot of J-Horror balances frights with implications of deeper terrors like you're looking for, such as Ringu, such that by the end that's where the strength of the movie lies.

In the Mouth of Madness

The Birds

I'll second Don't Look Now, but I like the Du Maurier source story a lot more than the movie, though it is certainly worth watching. I'll also second the other person's comments about watching the movie.

If you want something with a good dose of comedy with the horror, Cabin in the Woods fits your criteria pretty well too.